Method and apparatus for continuous assessment of a cardiovascular parameter using the arterial pulse pressure propagation time and waveform

ABSTRACT

A method and apparatus for determining a cardiovascular parameter including receiving an input signal corresponding to an arterial blood pressure measurement over an interval that covers at least one cardiac cycle, determining a propagation time of the input signal, determining at least one statistical moment of the input signal, and determining an estimate of the cardiovascular parameter using the propagation time and the at least one statistical moment.

CLAIM OF PRIORITY

The present application for patent is a Divisional of U.S. patentapplication Ser. No. 11/593,247, filed Nov. 6, 2006, entitled “METHODAND APPARATUS FOR CONTINUOUS ASSESSMENT OF A CARDIOVASCULAR PARAMETERUSING THE ARTERIAL PULSE PRESSURE PROPAGATION TIME AND WAVEFORM,” andclaims priority to U.S. Provisional Application No. 60/830,735, filedJul. 13, 2006, entitled “METHOD AND APPARATUS FOR CONTINUOUS ASSESSMENTOF A CARDIOVASCULAR PARAMETER USING THE ARTERIAL PULSE PRESSUREPROPAGATION TIME AND WAVEFORM,” and assigned to the assignee hereof andhereby expressly incorporated by reference herein.

FIELD OF THE INVENTION

The invention relates generally to a system and method for hemodynamicmonitoring. More particularly, the invention relates to a system andmethod for estimation of at least one cardiovascular parameter, such asvascular tone, arterial compliance or resistance, stroke volume (SV),cardiac output (CO), etc., of an individual using a measurement of anarterial pulse pressure propagation time and a waveform.

DESCRIPTION OF THE RELATED ART

Cardiac output (CO) is an important indicator not only for diagnosis ofdisease, but also for continuous monitoring of the condition of bothhuman and animal subjects, including patients. Few hospitals aretherefore without some form of conventional equipment to monitor cardiacoutput.

One way to measure CO is using the well-known formula:

CO=HR*SV,  (Equation 1)

where SV represents the stroke volume and HR represents the heart rate.The SV is typically measured in liters and the HR is typically measuredin beats per minute, although other units of volume and time may beused. Equation 1 expresses that the amount of blood the heart pumps outover a unit of time (such as a minute) is equal to the amount it pumpsout on every beat (stroke) times the number of beats per time unit.

Since the HR is easy to measure using a wide variety of instruments, thecalculation of CO usually depends on some technique for estimating theSV. Conversely, any method that directly yields a value for CO can beused to determine the SV by dividing by the HR. Estimates of CO or SVcan then be used to estimate, or contribute to estimating, any parameterthat can be derived from either of these values.

One invasive method to determine CO (or equivalently SV) is to mount aflow-measuring device on a catheter, and then to thread the catheterinto the subject and to maneuver it so that the device is in or near thesubject's heart. Some such flow-measuring devices inject either a bolusof material or energy (usually heat) at an upstream position, such as inthe right atrium, and determine flow based on the characteristics of theinjected material or energy at a downstream position, such as in thepulmonary artery. Patents that disclose implementations of such invasivetechniques (in particular, thermodilution) include:

-   U.S. Pat. No. 4,236,527 (Newbower et al., 2 Dec. 1980);-   U.S. Pat. No. 4,507,974 (Yelderman, 2 Apr. 1985);-   U.S. Pat. No. 5,146,414 (McKown et al., 8 Sep. 1992); and-   U.S. Pat. No. 5,687,733 (McKown et al., 18 Nov. 1997).

Still other invasive devices are based on the known Fick technique,according to which CO is calculated as a function of oxygenation ofarterial and mixed venous blood. In most cases, oxygenation is sensedusing right-heart catheterization. There have, however, also beenproposals for systems that non-invasively measure arterial and venousoxygenation, in particular, using multiple wavelengths of light; but todate they have not been accurate enough to allow for satisfactory COmeasurements on actual patients.

Invasive methods have obvious disadvantages. One such disadvantage isthat the catheterization of the heart is potentially dangerous,especially considering that the subjects (especially intensive carepatients) on which it is performed are often already in the hospitalbecause of some actually or potentially serious condition. Invasivemethods also have less obvious disadvantages. One such disadvantage isthat thermo-dilution relies on assumptions such as uniform dispersion ofthe injected heat that affects the accuracy of the measurementsdepending on how well they are fulfilled. Moreover, the introduction ofan instrument into the blood flow may affect the value (for example,flow rate) that the instrument measures. Therefore, there has been along-standing need for a method of determining CO that is bothnon-invasive (or at least as minimally invasive as possible) andaccurate.

One blood characteristic that has proven particularly promising foraccurately determining CO less invasively or non-invasively is bloodpressure. Most known blood pressure based systems rely on the pulsecontour method (PCM), which calculates an estimate of CO fromcharacteristics of the beat-to-beat arterial pressure waveform. In thePCM, “Windkessel” (German for “air chamber”) parameters (characteristicimpedance of the aorta, compliance, and total peripheral resistance) areused to construct a linear or non-linear hemodynamic model of the aorta.In essence, blood flow is analogized to a flow of electrical current ina circuit in which an impedance is in series with a parallel-connectedresistance and capacitance (compliance).

The three required parameters of the model are usually determined eitherempirically, through a complex calibration process, or from compiled“anthropometric” data, that is, data about the age, sex, height, weight,etc., of other patients or test subjects. U.S. Pat. No. 5,400,793(Wesseling, 28 Mar. 1995) and U.S. Pat. No. 5,535,753 (Petrucelli etal., 16 Jul. 1996) are representative of systems that utilize aWindkessel circuit model to determine CO.

Many extensions to the simple two-element Windkessel model have beenproposed in hopes of better accuracy. One such extension was developedby the Swiss physiologists Broemser and Ranke in their 1930 article“Ueber die Messung des Schlagvolumens des Herzens auf unblutigem Wegf,”Zeitung für Biologie 90 (1930) 467-507. In essence, the Broemsermodel—also known as a three-element Windkessel model—adds a thirdelement to the basic two-element Windkessel model to simulate resistanceto blood flow due to the aortic or pulmonary valve.

PCM systems can monitor CO more or less continuously, without the needfor a catheter to be left in the patient. Indeed, some PCM systemsoperate using blood pressure measurements taken using a finger cuff. Onedrawback of PCM systems, however, is that they are no more accurate thanthe rather simple, three-parameter model from which they are derived; ingeneral, a model of a much higher order would be needed to accuratelyaccount for other phenomena, such as the complex pattern of pressurewave reflections due to multiple impedance mis-matches caused by, forexample, arterial branching. Other improvements have therefore beenproposed, with varying degrees of complexity.

The “Method and Apparatus for Measuring Cardiac Output” disclosed bySalvatore Romano in U.S. Pat. No. 6,758,822, for example, represents adifferent attempt to improve upon PCM methods by estimating the SV,either invasively or non-invasively, as a function of the ratio betweenthe area under the entire pressure curve and a linear combination ofvarious components of impedance. In attempting to account for pressurereflections, the Romano system relies not only on accurate estimates ofinherently noisy derivatives of the pressure function, but also on aseries of empirically determined, numerical adjustments to a meanpressure value.

At the core of several methods for estimating CO is an expression of theform:

CO=HR*(K*SV_(est))  (Equation 2)

where RR is the heart rate, SV_(est) is the estimated stroke volume, andK is a scaling factor related to arterial compliance. Romano andPetrucelli, for example, rely on this expression, as do the apparatusesdisclosed in U.S. Pat. No. 6,071,244 (Band et al., 6 Jun. 2000) and U.S.Pat. No. 6,348,038 (Band et al., 19 Feb. 2002).

Another expression often used to determines CO is:

CO=MAP*C/tau  (Equation 3)

where MAP is mean arterial pressure, tau is an exponential pressuredecay constant, and C, like K, is a scaling factor related to arterialcompliance K. U.S. Pat. No. 6,485,431 (Campbell, 26 Nov. 2002) disclosesan apparatus that uses such an expression.

The accuracy of these methods may depend on how the scaling factors Kand C are determined. In other words, an accurate estimate of compliance(or of some other value functionally related to compliance) may berequired. For example, Langwouters (“The Static Elastic Properties of 45Human Thoracic and 20 Abdominal Aortas in vitro and the Parameters of aNew Model,” J. Biomechanics, Vol. 17, No. 6, pp. 425-435, 1984)discusses the measurement of vascular compliance per unit length inhuman aortas and relates it to a patient's age and sex. An aortic lengthis determined to be proportional to a patient's weight and height. Anomogram, based on this patient information, is then derived and used inconjunction with information derived from an arterial pressure waveformto improve an estimate of the compliance factor.

It is likely that the different prior art apparatuses identified above,each suffer from one or more drawbacks. The Band apparatus, for example,requires an external calibration using an independent measure of CO todetermine a vascular impedance-related factor that is then used in COcalculations. U.S. Pat. No. 6,315,735 (Joeken et al., 13 Nov. 2001)describes another device with the same shortcoming.

Wesseling (U.S. Pat. No. 5,400,793, 28 Mar. 1995) attempts to determinea vascular compliance-related factor from anthropometric data such as apatient's height, weight, sex, age, etc. This method relies on arelationship that is determined from human nominal measurements and maynot apply robustly to a wide range of patients.

Romano attempts to determine a vascular impedance-related factor solelyfrom features of the arterial pressure waveform, and thus fails to takeadvantage of known relationships between patient characteristics andcompliance. In other words, by freeing his system of a need foranthropometric data, Romano also loses the information contained in suchdata. Moreover, Romano bases several intermediate calculations on valuesof the derivatives of the pressure waveform. As is well known, however,such estimates of derivatives are inherently noisy. Romano's method has,consequently, been unreliable.

What is needed is a system and method for more accurately and robustlyestimating cardiovascular parameters such as arterial compliance (K orC) or resistance, vascular tone, tau, or values computed from theseparameters, such as the SV and the CO.

One of the present inventors earlier published that the SV can beapproximated as being proportional to the standard deviation of thearterial pressure waveform P(t), or of some other signal that itself isproportional to P(t): U.S. Published Patent Application No. 2005/0124903A1 (Luchy Roteliuk et al., 9 Jun. 2005, “Pressure based System andMethod for Determining Cardiac Stroke Volume”). Thus, one way toestimate the SV is to apply the relationship:

SV=Kσ(P)=K std(P)  (Equation 4)

where K is a scaling factor and from which follows:

CO=Kσ(P)HR=K std(P)HR  (Equation 5)

This proportionality between the SV and the standard deviation of thearterial pressure waveform is based on the observation that thepulsatility of a pressure waveform is created by the cardiac SV into thearterial tree as a function of the vascular tone (i.e., vascularcompliance and peripheral resistance). The scaling factor K of equations4 and 5 is an estimate of the vascular tone.

Recently, one of the present inventors also published that vascular tonecan be reliably estimated using the shape characteristics of thearterial pulse pressure waveform in combination with a measure of thepressure dependant vascular compliance and the patient's anthropometricdata such as age, gender, height, weight and body surface area (BSA):U.S. Published Patent No. 2005/0124904 A1 (Luchy Roteliuk, 9 Jun. 2005,“Arterial pressure-based automatic determination of a cardiovascularparameter”). To quantify the shape information of the arterial pulsepressure waveform, he used higher order time domain statistical momentsof the arterial pulse pressure waveform (such as kurtosis and skewness)in addition to the newly derived pressure weighted statistical moments.Thus, the vascular tone is computed as a function of a combination ofparameters using a multivariate regression model with the followinggeneral form:

K=χ(μ_(T1),μ_(T2), . . . μ_(Tk),μ_(P1),μ_(P2), . . . μ_(Pk),C(P),BSA,Age,G . . . )  (Equation 6)

where

K is vascular tone (the calibration factor in equations 4 and 5);

X is a multiregression statistical model;

μ_(1T) . . . μ_(kT) are the 1-st to k-th order time domain statisticalmoments of the arterial pulse pressure waveform;

μ_(1P) . . . μ_(kP) are the 1-st to k-th order pressure weightedstatistical moments of the arterial pulse pressure waveform;

C(P) is a pressure dependent vascular compliance computed using methodsproposed by Langwouters et al 1984 (“The Static Elastic Properties of 45Human Thoracic and 20 Abdominal Aortas in vitro and the Parameters of aNew Model,” J. Biomechanics, Vol. 17, No. 6, pp. 425-435, 1984);

BSA is a patient's body surface area (function of height and weight);

Age is a patient's age; and

G is a patient's gender.

The predictor variables set for computing the vascular tone factor K,using the multivariate model χ, were related to the “true” vascular tonemeasurement, determined as a function of CO measured throughthermo-dilution and the arterial pulse pressure, for a population oftest or reference subjects. This creates a suite of vascular tonemeasurements, each of which is a function of the component parameters ofχ. The multivariate approximating function is then computed, using knownnumerical methods, that best relates the parameters of χ to a givensuite of CO measurements in some predefined sense. A polynomialmultivariate fitting function is used to generate the coefficients ofthe polynomial that gives a value of χ for each set of the predictorvariables. Thus, the multivariate model has the following general form:

$\begin{matrix}{\chi = {\begin{bmatrix}A_{1} & A_{2} & \ldots & A_{n}\end{bmatrix}*\begin{bmatrix}X_{1} \\X_{2} \\\ldots \\X_{n}\end{bmatrix}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$

where A₁ . . . A_(n) are the coefficients of the polynomialmultiregression model, and X are the model's predictor variables:

$\begin{matrix}{X_{n,1} = {\prod\limits_{m}^{\;}\; \left( \begin{bmatrix}{\mu_{T\; 1}\mspace{14mu} \ldots} & \mu_{Tk} & {\mu_{P\; 1}\mspace{14mu} \ldots} & {\mu_{P\; 1}\mspace{14mu} \ldots} & {\mu_{Tk}{C(P)}} & {BSA} & {Age} & G & \ldots\end{bmatrix}^{\bigwedge{\lbrack\begin{matrix}P_{1,1} & \ldots & P_{1,m} \\\ldots & \ldots & \ldots \\P_{n,1} & \ldots & P_{n,m}\end{matrix}\rbrack}} \right)}} & \left( {{Equation}\mspace{14mu} 8} \right)\end{matrix}$

The method listed above relies solely on a single arterial pulsepressure measurement. Its simplicity and the fact that it does notrequire a calibration are advantages of this method. However, due to theempirical nature of the vascular tone assessment relationships, theaccuracy of this method may be low in some extreme clinical situationswhere the basic empirical relationships of the model are not valid. Forthis reason, a second independent measurement may be beneficial if addedto the basic multiregression model.

As shown above, many techniques have been devised, both non-invasive andinvasive, for measuring the SV and CO, and particularly for detectingvascular compliance, peripheral resistance and vascular tone. It shouldbe appreciated that there is a need for a system and method forestimating CO, or any parameter that can be derived from or using CO,that is robust and accurate and that is less sensitive to calibrationand computational errors.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of two blood pressure curves representingtwo different arterial pressure measurements received from a subjectaccording to an embodiment of the invention.

FIG. 2 illustrates an example of an Electrocardiogram measurement (ECG)and a blood pressure measurement received from a subject according to anembodiment of the invention.

FIG. 3 is a graph illustrating the relationship between the arterialpulse pressure propagation time and the arterial compliance according toan embodiment of the invention.

FIG. 4 is a graph illustrating the relationship between the pulsepressure propagation time and vascular tone on patients recovering fromcardiac arrest according to an embodiment of the invention.

FIGS. 5-6 are graphs illustrating the correlation between the pulsepressure propagation time and vascular tone for different hemodynamicconditions of the subjects according to several embodiments of theinvention.

FIGS. 7-9 are graphs illustrating the correlation between the COcomputed using the pulse pressure propagation time, Continuous CardiacOutput (CCO) and CO values measured by thermodilution bolus measurements(TD-CO) for different hemodynamic states of the subjects according toseveral embodiments of the invention.

FIG. 10 is a graph showing the relationship between the CO estimatedusing the arterial pressure propagation time according to severalembodiments of the invention and CO estimated using the arterial pulsepressure signal.

FIG. 11 is a block diagram showing an exemplary system used to executethe various methods described herein according to several embodiments ofthe invention.

FIG. 12 is a flow chart showing a method according to an embodiment ofthe invention.

SUMMARY OF THE INVENTION

One embodiment of the invention provides a method for determining acardiovascular parameter including receiving an input signalcorresponding to an arterial blood pressure measurement over an intervalthat covers at least one cardiac cycle, determining a propagation timeof the input signal, determining at least one statistical moment of theinput signal, and determining an estimate of the cardiovascularparameter using the propagation time and the at least one statisticalmoment.

One embodiment of the invention provides an apparatus for determining acardiovascular parameter including a processing unit to receive an inputsignal corresponding to an arterial blood pressure measurement over aninterval that covers at least one cardiac cycle, determine a propagationtime of the input signal, determine at least one statistical moment ofthe input signal and determine an estimate of the cardiovascularparameter using the propagation time and the at least one statisticalmoment.

DETAILED DESCRIPTION

Methods and systems that implement the embodiments of the variousfeatures of the invention will now be described with reference to thedrawings. The drawings and the associated descriptions are provided toillustrate embodiments of the invention and not to limit the scope ofthe invention. Reference in the specification to “one embodiment” or “anembodiment” is intended to indicate that a particular feature,structure, or characteristic described in connection with the embodimentis included in at least an embodiment of the invention. The appearancesof the phrase “one embodiment” or “an embodiment” in various places inthe specification are not necessarily all referring to the sameembodiment. Throughout the drawings, reference numbers are re-used toindicate correspondence between referenced elements.

In broadest terms, the invention involves the determination of a cardiacvalue, such as a stroke volume (SV), and/or a value derived from the SVsuch as cardiac output (CO), using the arterial pulse pressurepropagation time. The arterial pulse pressure propagation time may bemeasured by using arterial pressure waveforms or waveforms that areproportional to or derived from the arterial pulse pressure,electrocardiogram measurements, bioimpedance measurements, othercardiovascular parameters, etc. These measurements may be made with aninvasive, non-invasive or minimally invasive instrument or a combinationof instruments.

The invention may be used with any type of subject, whether human oranimal. Because it is anticipated that the most common use of theinvention will be on humans in a diagnostic setting, the invention isdescribed below primarily in use with a “patient.” This is by way ofexample only; however, it is intended that the term “patient” shouldencompass all subjects, both human and animal, regardless of setting.

FIG. 1 illustrates an example of two blood pressure curves representingtwo different arterial pressure measurements received from a subject.The top curve represents a central arterial pressure measurementdetected from the subject's aorta and the bottom curve represents ameasurement detected from the subject's radial artery. The pulsepressure propagation time (t_(prop)) can be measured as the transit timebetween the two arterial pressure measurements.

The rationale of using the pulse pressure propagation time forhemodynamic measurements is based on a basic principle of cardiovascularbiomechanics. That is, if the subject's heart pumped blood through acompletely rigid vessel, upon contraction of the heart, the pressurewaveform would instantaneously be present at any distal arteriallocation in the subject's body. However, if the subject's heart pumpedblood through a compliant vessel, upon contraction of the heart, thepressure waveform would be present some amount of time after the heartcontracted at a distal arterial location in the subject's body.

The pulse pressure propagation time can be measured invasively ornon-invasively at several different locations on the pressure waveform(or any other waveform related to the pressure waveform). In the exampleshown on FIG. 1, the pulse pressure propagation time may be measured byusing two different arterial pressure measurements, for example, onereference measurement from the aorta and one peripheral measurement fromthe radial artery.

FIG. 2 illustrates an example of using an electrocardiogram signal as areference signal for the propagation time measurement. The top curverepresents an electrocardiogram (ECG) signal detected with electrodesplaced near the subject's heart and the bottom curve represents anarterial pressure measurement detected from the subject's peripheralartery. In this example, the arterial pulse pressure propagation time(t_(prop)) may be measured by using the transit time between the ECGsignal and the peripheral arterial pressure. Similarly, a transthoracicbioimpedance measurement could be used as a reference site, and thepropagation time could be measured as a transit time versus a peripheralmeasurement derived from or proportional to the arterial blood pressure.

The arterial pulse pressure propagation time provides an indirectmeasure of the physical (i.e., mechanical) properties of a vesselsegment between the two recording sites. These properties includeprimarily the elastic and geometric properties of the arterial walls.The properties of the arterial walls, for example their thicknesses andlumen diameters, are some of the major determinants of the arterialpulse pressure propagation time. As a result, the pulse pressurepropagation time depends mainly on the arterial compliance.

FIG. 3 illustrates an example where the pulse pressure propagation timeincreases with increasing arterial compliance (C). Hence, the pulsepressure propagation time (t_(prop)) can be represented as a function ofarterial compliance (C), i.e.,

t _(prop) =f(C)  (Equation 9)

The arterial pulse pressure propagation time can therefore be used as asimple measure to estimate the arterial compliance. The propagation timecan be used as a separate measure to assess a patient's vascular statusor can be used in a pulse contour cardiac output algorithm along withother parameters to account for the effects of vascular compliance,vascular resistance and vascular tone. In one embodiment, the arterialpulse pressure propagation time is measured using an arterial pulsepressure signal from relatively large arteries (e.g., radial, femoral,etc.) and therefore the influence of the peripheral resistance isminimal. Also, this measurement may include the average arterialcompliance between the measurement sites and may not reflect thepressure dependence of the arterial compliance.

The basic relationship could be derived from the well knownBramwell-Hill equation used to calculate the pulse wave velocity (PWV):

$\begin{matrix}{{PWV}^{2} = {\frac{P}{V} \cdot \frac{1}{\rho} \cdot V}} & \left( {{Equation}\mspace{14mu} 10} \right)\end{matrix}$

where

dP is the change in pressure;

dV is the change in volume;

ρ is the blood density; and

V is the baseline volume.

The arterial compliance (C) may be defined as the ratio of theincremental change in volume (dV) resulting from an incremental changein pressure (dP), i.e.,

$\begin{matrix}{C = \frac{V}{P}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

Substituting equation (11) into equation (10), we obtain the followingequation:

$\begin{matrix}{{PWV}^{2} = {\frac{1}{C} \cdot \frac{1}{\rho} \cdot V}} & \left( {{Equation}\mspace{14mu} 12} \right)\end{matrix}$

On the other hand PWV is defined as follows:

$\begin{matrix}{{PWV} = \frac{L}{t_{prop}}} & \left( {{Equation}\mspace{14mu} 13} \right)\end{matrix}$

where L is the vascular length between the two recording sites andt_(prop) is the arterial pulse pressure propagation time.

If equation 13 is substituted into equation 12, the arterial compliancecan be given by:

$\begin{matrix}{C = {\frac{1}{L^{2}} \cdot \frac{1}{\rho} \cdot V \cdot t_{prop}^{2}}} & \left( {{Equation}\mspace{14mu} 14} \right)\end{matrix}$

If we define γ as:

$\begin{matrix}{\gamma = {\frac{1}{L^{2}} \cdot \frac{1}{\rho} \cdot V}} & \left( {{Equation}\mspace{14mu} 15} \right)\end{matrix}$

The arterial compliance can be represented as:

C=γ·t _(prop) ²  (Equation 16)

where the scaling factor γ is a function, which depends on the blooddensity, the effective vascular distance between the two recording sitesand the basic volume, i.e., γ depends on the physical vascular volumebetween the two recording site and the blood viscosity (i.e., Hematocrit. . . etc).

Based on the above equations, the arterial pulse pressure propagationtime can be used in a number of different ways. The pulse pressurepropagation time may be used as an input to a hemodynamic model based onthe standard deviation of the arterial pulse pressure to evaluate thedynamic changes in the arterial pressure created by the systolicejection. The CO can be represented as a function of the standarddeviation of the arterial pulse pressure as follows:

CO=K*std(P)*HR  (Equation 17)

where K, as we have shown above, is a scaling factor proportional to thearterial compliance, std(P) is the standard deviation of the arterialpulse pressure, and HR is the heart rate.

It is also understood that:

$\begin{matrix}{{CO} = {C \cdot \frac{MAP}{\tau}}} & \left( {{Equation}\mspace{14mu} 18} \right)\end{matrix}$

where MAP is the mean arterial pressure, τ is an exponential pressuredecay constant, and C, like K, is a scaling factor related to arterialcompliance.

From equations 17 and 18, the scaling factor K is a measure equal tovascular compliance. If we substitute the scaling factor K in equation17 for the compliance as given in equation 16, CO can be computed usingthe standard deviation of the arterial pulse pressure waveform and thearterial pulse pressure propagation time:

CO=γ·t _(prop) ²·std(P)·HR  (Equation 19)

where standard deviation of the arterial pulse pressure can becalculated using the equation:

$\begin{matrix}{{{std}\mspace{14mu} (P)} = \sqrt{\frac{1}{n - 1}{\sum\limits_{k = 1}^{n}\; \left\lbrack {{P(k)} - P_{avg}} \right\rbrack^{2}}}} & \left( {{Equation}\mspace{14mu} 20} \right)\end{matrix}$

where n is the total number of samples, P(k) is the instantaneous pulsepressure, and P_(avg) is the mean arterial pressure. The mean arterialpressure can be defined as:

$\begin{matrix}{P_{avg} = {\frac{1}{n}{\sum\limits_{k = 1}^{n}\; {P(k)}}}} & \left( {{Equation}\mspace{14mu} 21} \right)\end{matrix}$

FIG. 4 is a graph illustrating the relationship between the square ofthe arterial pulse pressure propagation time and the scaling factor K ofpatients during recovery from cardiac bypass surgery. FIG. 4 plots ten(10) averaged data points from ten (10) different patients. In theexample of FIG. 4, the arterial pulse pressure propagation time has beencalculated as a transit time between the ECG signal and the radialarterial pressure. The data shown in FIG. 4 illustrates that the Kscaling factors of equation 17 can be effectively estimated using thearterial pulse pressure propagation time as given by equation 16.

FIGS. 5 and 6 are graphs illustrating the correlation between thearterial pulse pressure propagation time and the K scaling factor ofequation 17 for different hemodynamic states of two subjects. Bothtrends correspond to animal data taken from experiments using porcineanimal models. These figures show identical trends of the scaling factorK and the square of the pulse pressure propagation time. The data onFIGS. 5 and 6 illustrate that the K or the C scaling factors ofequations 17 and 18 can be effectively estimated using the arterialpulse pressure propagation time.

The scaling factor γ of equation 19 can be determined using anypre-determined function of the propagation time and the pressure P(t);thus,

γ=Γ(t _(prop) ,P)  (Equation 22)

where Γ is a pre-determined function of the propagation time andpressure, used to develop computational methods to estimate γ.

Any known, independent CO technique may be used to determine thisrelationship, whether invasive, for example, thermodilution, ornon-invasive, for example, trans-esophageal echocardiography (TEE) orbio-impedance measurement. The invention provides continuous trending ofCO between intermittent measurements such as TD or TEE.

Even if an invasive technique such as catheterization is used todetermine γ, it will usually not be necessary to leave the catheter inthe patient during the subsequent CO-monitoring session. Moreover, evenwhen using a catheter-based calibration technique to determine γ, it isnot necessary for the measurement to be taken in or near the heart;rather, the calibration measurement can be made in the femoral artery.As such, even where an invasive technique is used to determine γ, theinvention as a whole is still minimally invasive in that anycatheterization may be peripheral and temporary.

As discussed above, rather than measure arterial blood pressuredirectly, any other input signal may be used that is proportional toblood pressure. This means that calibration may be done at any or all ofseveral points in the calculations. For example, if some signal otherthan arterial blood pressure itself is used as an input signal, then itmay be calibrated to blood pressure before its values are used tocalculate standard deviation, or afterwards, in which case either theresulting standard deviation value can be scaled, or the resulting SVvalue can be calibrated (for example, by setting γ properly), or somefinal function of SV (such as CO) can be scaled. In short, the fact thatthe invention may in some cases use a different input signal than adirect measurement of arterial blood pressure does not limit its abilityto generate an accurate SV estimate.

In addition to the blood viscosity, γ depends mainly of the physicalvascular volume between the two recording sites. Of course, theeffective length (L) and the effective volume (V) between the tworecording sites can not be known. Vascular branching and the patient topatient differences are two main reasons why the effective physicalvascular volume between the two recording sites can not be known.However, it is obvious that this physical volume is proportional to thepatient's anthropometric parameters and therefore it can be estimatedindirectly using the patient's anthropometric parameters. Theanthropometric parameters may be derived from various parameters such asthe measured distance (l) between the two recording sites, patient'sweight, patient's height, patient's gender, patient's age, patient'sbsa, etc., or any combination of these factors. In one embodiment, allthe anthropometric parameters, for example, the distance (l) between thetwo recording sites, patient's weight, patient's height, patient'sgender, patient's age and patient's bsa, may be used to compute γ.Additional values are preferably also included in the computation totake other characteristics into account. In one embodiment, the heartrate HR (or period of R-waves) may be used. Thus,

γ=Γ_(M)(l,H,W,BSA,Age,G,HR)  (Equation 23)

Where

l is the measured distance between the two recording sites;

H is the patient's height;

W is the patient's weight;

BSA is the patient's bsa;

Age is the patient's age;

G is the patient's gender;

HR is the patient's heart rate; and

Γ_(M) is a multivariate model.

The predictor variables set for computing γ, using the multivariatemodel Γ, are related to the “true” vascular compliance measurement,determined as a function of CO measured through thermo-dilution and thearterial pulse pressure, for a population of test or reference subjects.This creates a suite of compliance measurements, each of which is afunction of the component parameters of Γ_(M). The multivariateapproximating function is then computed using numerical methods thatbest relates the parameters of Γ_(M) to a given suite of CO measurementsin a predefined manner. A polynomial multivariate fitting function isused to generate the coefficients of the polynomial that give a value ofΓ_(M) for each set of the predictor variables. Thus, the multivariatemodel has the following general equation:

$\begin{matrix}{\Gamma_{M} = {\left\lbrack {a_{1}\mspace{14mu} a_{2}\mspace{14mu} \ldots \mspace{14mu} a_{n}} \right\rbrack*\begin{bmatrix}Y_{1} \\Y_{2} \\\ldots \\Y_{n}\end{bmatrix}}} & \left( {{Equation}\mspace{14mu} 24} \right)\end{matrix}$

where a₁ . . . a_(n) are the coefficients of the polynomialmultiregression model, and Y are the model's predictor variables:

$\begin{matrix}{Y_{n,1} = {\prod\limits_{m}\; \left( {\left\lbrack {l\mspace{14mu} H\mspace{14mu} W\mspace{14mu} {BSA}\mspace{14mu} {Age}\mspace{14mu} G\mspace{14mu} {HR}} \right\rbrack^{\hat{}}}^{\lbrack\begin{matrix}P_{1,1} & \ldots & P_{1,m} \\\ldots & \ldots & \ldots \\P_{n,1} & \ldots & P_{n,m}\end{matrix}\rbrack} \right)}} & \left( {{Equation}\mspace{14mu} 25} \right)\end{matrix}$

The use of the arterial pulse pressure propagation time to estimatevascular tone. Vascular tone is a hemodynamic parameter used to describethe combined effect of vascular compliance and peripheral resistance. Inthe prior art, the shape characteristics of the arterial pressurewaveform in combination with patients anthropometric data and othercardiovascular parameters were used to estimate vascular tone (seeRoteliuk, 2005, “Arterial pressure-based automatic determination of acardiovascular parameter”). The arterial pulse pressure propagation timecan also be used to estimate vascular tone. In one embodiment, thearterial pulse pressure propagation time can be used as an independentterm to a multivariate regression model to continuously estimatevascular tone. In one embodiment, the arterial pulse pressurepropagation time can be used in combination with the shape informationof the arterial pulse pressure waveform to estimate the vascular tone.The higher order shape sensitive arterial pressure statistical momentsand the pressure-weighted time moments may be used as predictorvariables in the multivariate model along with the arterial pulsepressure propagation time. Additional values are preferably alsoincluded in the computation to take other characteristics into account.For example, the heart rate HR (or period of R-waves), the body surfacearea BSA, as well as a pressure dependent non-linear compliance valueC(P) may be calculated using a known method such as described byLangwouters, which computes compliance as a polynomial function of thepressure waveform and the patient's age and sex. Thus,

K=χ(t _(prop),μ_(T1),μ_(T2), . . . μ_(Tk),μ_(P1),μ_(P2), . . . μ_(Pk),C(P),BSA,Age,G . . . )  (Equation 6)

where

K is vascular tone;

X is a multiregression statistical model;

t_(prop) is the arterial pulse pressure propagation time;

μ_(1T) . . . μ_(kT) are the 1-st to k-th order time domain statisticalmoments of the arterial pulse pressure waveform;

μ_(1P) . . . μ_(kP) are the 1-st to k-th order pressure weightedstatistical moments of the arterial pulse pressure waveform;

C(P) is the pressure dependent vascular compliance as defined byLangwouters et al. (“The Static Elastic Properties of 45 Human Thoracicand 20 Abdominal Aortas in vitro and the Parameters of a New Model,” J.Biomechanics, Vol. 17, No. 6, pp. 425-435, 1984); BSA is the patient'sbody surface area (function of height and weight);

Age is the patient's age; and

Gender is the patient's gender.

Depending on the needs of a given implementation of the invention, onemay choose not to include either skewness or kurtosis, or one mayinclude even higher order moments. The use of the first four statisticalmoments has proven successful in contributing to an accurate and robustestimate of compliance. Moreover, anthropometric parameters other thanthe HR and BSA may be used in addition, or instead, and other methodsmay be used to determine C(P), which may even be completely omitted.

The exemplary method described below for computing a current vasculartone value may be adjusted in a known manner to reflect the increased,decreased, or altered parameter set. Once the parameter set forcomputing K has been assembled, it may be related to a known variable.Existing devices and methods, including invasive techniques, such asthermo-dilution, may be used to determine CO, HR and SV_(est) for apopulation of test or reference subjects. For each subject,anthropometric data such as age, weight, BSA, height, etc. can also berecorded. This creates a suite of CO measurements, each of which is afunction (initially unknown) of the component parameters of K. Anapproximating function can therefore be computed, using known numericalmethods, that best relates the parameters to K given the suite of COmeasurements in some predefined sense. One well understood and easilycomputed approximating function is a polynomial. In one embodiment, astandard multivariate fitting routine is used to generate thecoefficients of a polynomial that gave a value of K for each set ofparameters t_(prop), HR, C(P), BSA, μ_(1P), σ_(P), μ_(3P), μ_(4P)μ_(1T), σ_(T), μ_(3T), μ_(4T).

In one embodiment, K is computed as follows:

$\begin{matrix}{K = {\left\lbrack {A_{1}\mspace{14mu} A_{2}\mspace{14mu} \ldots \mspace{14mu} A_{n}} \right\rbrack*\begin{bmatrix}X_{1} \\X_{2} \\\ldots \\X_{n}\end{bmatrix}}} & \left( {{Equation}\mspace{14mu} 27} \right)\end{matrix}$

where

$\begin{matrix}{X_{n,1} = {\prod\limits_{m}\; \left( \left\lbrack {t_{prop},\mu_{T\; 1},\mu_{T\; 2},{\ldots \mspace{14mu} \mu_{T\; 2}},\mu_{P\; 1},\mu_{P\; 2},{\ldots \mspace{14mu} \mu_{Pk}},{C(P)},{BSA},{Age},{G\mspace{14mu} \ldots}} \right\rbrack^{\hat{}^{\lbrack\begin{matrix}P_{1,1} & \ldots & P_{1,m} \\\ldots & \ldots & \ldots \\P_{n,1} & \ldots & P_{n,m}\end{matrix}\rbrack}} \right)}} & \left( {{Equation}\mspace{14mu} 28} \right)\end{matrix}$

The use of the arterial pulse pressure propagation to directly estimateCO is discussed below.

The pulse pressure propagation time may be used as an independent methodto estimate CO. That is, the arterial pulse pressure propagation time isindependently proportional to SV, as shown below:

$\begin{matrix}{{SV} = {K_{p} \cdot \frac{1}{t_{prop}}}} & \left( {{Equation}\mspace{14mu} 29} \right)\end{matrix}$

CO can be estimated if we multiply equation 29 by HR:

$\begin{matrix}{{CO} = {K_{p} \cdot \frac{1}{t_{prop}} \cdot {HR}}} & \left( {{Equation}\mspace{14mu} 30} \right)\end{matrix}$

The scaling factor K_(p) can be estimated using a direct calibration,for example, using a known CO value from a bolus thermo-dilutionmeasurement or other gold standard CO measurement. FIGS. 7-9 are graphsillustrating the correlation between the CO computed using the pulsepressure propagation time as shown in equation 30 (COprop), ContinuousCardiac Output (CCO) and CO values measured by intermittentthermodilution bolus measurements (ICO). CCO and ICO are measured usingthe Vigilance monitor manufactured by Edwards Lifesciences of Irvine,Calif. The measurements have been performed on animal porcine models indifferent hemodynamic states of the animals. These graphs showexperimentally that changes in CO are related to changes in the pulsepressure propagation time and that the pulse pressure propagation timecan be used as an independent method to estimate CO.

The scaling factor K_(p) of equation 30 can be determined using anypre-determined function of the propagation time and CO or SV. Anyindependent CO technique may be used to determine this relationship,whether invasive, for example, thermo-dilution, or non-invasive, forexample, trans-esophageal echocardiography (TEE) or bio-impedancemeasurement. The invention provides continuous trending of CO betweenintermittent measurements such as TD or TEE.

Even if an invasive technique such as catheterization is used todetermine K_(p), it may not be necessary to leave the catheter in thepatient during the subsequent CO-monitoring session. Moreover, even whenusing catheter-based calibration technique to determine K_(p), it maynot be necessary for the measurement to be taken in or near the heart;rather, the calibration measurement can be made in the femoral artery.As such, even where an invasive technique is used to determine K_(p),the method is still minimally invasive in that any catheterization maybe peripheral and temporary.

The approach shown in equation 30 allows measuring CO to be performedcompletely non-invasively if non-invasive techniques are used to measurethe propagation time and if a predefined function or relationship isused to measure K_(p). The non-invasive techniques to measure thepropagation time can include, but are not limited to: ECG, non-invasivearterial blood pressure measurements, bio-impedance measurements,optical pulse oximetry measurements, Doppler ultrasound measurements, orany other measurements derived from or proportional to them or anycombination of them (for example: using Doppler ultrasound pulsevelocity measurement to measure the reference signal near the heart andusing a bio-impedance measurement to measure the peripheral signal . . .etc).

The scaling factor K_(p), depends mainly on blood viscosity and thephysical vascular distance and volume between the two recording sites.Of course, the effective length (L) and the effective volume (V) betweenthe two recording sites can not be known. Vascular branching and thepatient to patient differences are two main reasons why the effectivephysical vascular volume between the two recording sites can not beknown. However, the physical volume may be proportional to the patient'santhropometric parameters and therefore it can be estimated indirectlyusing the patient's anthropometric parameters. The anthropometricparameters may be derived from various parameters such as the measureddistance (L) between the two recording sites, patient's weight,patient's height, patient's gender, patient's age, patient's bsa etc.,or any combination of these parameters. In one embodiment, all theanthropometric parameters: the distance (L) between the two recordingsites, patient's weight, patient's height, patient's gender, patient'sage and patient's bsa are used to compute K_(p). Thus,

K _(p) =M(L,H,W,BSA,Age,G)  (Equation 31)

where

L is the measured distance between the two recording sites;

H is the patient's height;

W is the patient's weight;

BSA is the patient's bsa;

Age is the patient's age;

G is the patient's gender; and

M is a multivariate linear regression model.

The predictor variables set for computing K_(p), using the multivariatemodel M, are related to the “true” CO measurement, determined as afunction of the propagation time, where CO is measured throughthermo-dilution, for a population of test or reference subjects. Thiscreates a suite of measurements, each of which is a function of thecomponent parameters of M. The multivariate approximating function isthen computed using numerical methods that best relates the parametersof M to a given suite of CO measurements in some predefined sense. Apolynomial multivariate fitting function is used to generate thecoefficients of the polynomial that give a value of M for each set ofthe predictor variables. Thus, the multivariate model has the followingequation:

$\begin{matrix}{M = {\left\lbrack {a_{1}\mspace{14mu} a_{2}\mspace{14mu} \ldots \mspace{14mu} a_{n}} \right\rbrack*\begin{bmatrix}Y_{1} \\Y_{2} \\\ldots \\Y_{n}\end{bmatrix}}} & \left( {{Equation}\mspace{14mu} 32} \right)\end{matrix}$

where a₁ . . . a_(n) are the coefficients of the polynomialmultiregression model, and Y are the model's predictor variables:

$\begin{matrix}{Y_{n,1} = {\prod\limits_{m}\; \left( \left\lbrack {L\mspace{14mu} H\mspace{14mu} W\mspace{14mu} {BSA}\mspace{14mu} {Age}\mspace{14mu} G}\mspace{14mu} \right\rbrack^{\hat{}^{\lbrack\begin{matrix}P_{1,1} & \ldots & P_{1,m} \\\ldots & \ldots & \ldots \\P_{n,1} & \ldots & P_{n,m}\end{matrix}\rbrack}} \right)}} & \left( {{Equation}\mspace{14mu} 33} \right)\end{matrix}$

FIG. 10 is a graph showing the relationship between the CO estimatedusing equation 17 (CO_(std) on the x-axis) and CO estimated usingequation 30 (CO_(prop) on the y-axis) from a series of animalexperiments. The data shows CO measurements from a total of ten (10)pigs. Three (3) selected data points from each pig are used for thegraph. In order to cover a wide CO range, each selected data pointcorresponds to a different hemodynamic state of the pig: vasodilated,vasoconstricted and hypovolemic states, respectively. Theproportionality shown in FIG. 10 is experimental proof of theeffectiveness and the reliability of using the propagation time toestimate CO.

FIG. 11 is a block diagram showing an exemplary system used to executethe various methods described herein. The system may include a patient100, a pressure transducer 201, a catheter 202, ECG electrodes 301 and302, signal conditioning units 401 and 402, a multiplexer 403, ananalog-to-digital converter 405 and a computing unit 500. The computingunit 500 may include a patient specific data module 501, a scalingfactor module 502, a moment module 503, a standard deviation module 504,a propagation time module 505, a stroke volume module 506, a cardiacoutput module 507, a heart rate module 508, an input device 600, anoutput device 700, and a heart rate monitor 800. Each unit and modulemay be implemented in hardware, software, or a combination of hardwareand software.

The patient specific data module 501 is a memory module that storespatient data such as a patient's age, height, weight, gender, BSA, etc.This data may be entered using the input device 600. The scaling factormodule 502 receives the patient data and performs calculations tocompute the scaling compliance factor. For example, the scaling factormodule 502 puts the parameters into the expression given above or intosome other expression derived by creating an approximating function thatbest fits a set of test data. The scaling factor module 502 may alsodetermine the time window [t0, tf] over which each vascular compliance,vascular tone, SV and/or CO estimate is generated. This may be done assimply as choosing which and how many of the stored, consecutive,discretized values are used in each calculation.

The moment module 503 determines or estimates the arterial pulsepressure higher order statistical time domain and weighted moments. Thestandard deviation module 504 determines or estimates the standarddeviation of the arterial pulse pressure waveform. The propagation timemodule 505 determines or estimates the propagation time of the arterialpulse pressure waveform.

The scaling factor, the higher order statistical moments, the standarddeviation and the propagation time are input into the stroke volumemodule 506 to produce a SV value or estimate. A heart rate monitor 800or software routine 508 (for example, using Fourier or derivativeanalysis) can be used to measure the patient's heart rate. The SV valueor estimate and the patient's heart rate are input into the cardiacoutput module 507 to produce an estimate of CO using, for example, theequation CO=SV*HR.

As mentioned above, it may not be necessary for the system to compute SVor CO if these values are not of interest. The same is true for thevascular compliance, vascular tone and peripheral resistance. In suchcases, the corresponding modules may not be necessary and may beomitted. For example, the invention may be used to determined arterialcompliance. Nonetheless, as FIG. 11 illustrates, any or all of theresults, SV, CO, vascular compliance, vascular tone and peripheralresistance may be displayed on the output device 700 (e.g., a monitor)for presentation to and interpretation by a user. As with the inputdevice 600, the output device 700 may typically be the same as is usedby the system for other purposes.

The invention further relates to a computer program loadable in acomputer unit or the computing unit 500 in order to execute the methodof the invention. Moreover, the various modules 501-507 may be used toperform the various calculations and perform related method stepsaccording to the invention and may also be stored as computer-executableinstructions on a computer-readable medium in order to allow theinvention to be loaded into and executed by different processingsystems.

While certain exemplary embodiments have been described and shown in theaccompanying drawings, it is to be understood that such embodiments aremerely illustrative of and not restrictive on the broad invention, andthat this invention not be limited to the specific constructions andarrangements shown and described, since various other changes,combinations, omissions, modifications and substitutions, in addition tothose set forth in the above paragraphs, are possible. Those skilled inthe art will appreciate that various adaptations and modifications ofthe just described preferred embodiment can be configured withoutdeparting from the scope and spirit of the invention. Therefore, it isto be understood that, within the scope of the appended claims, theinvention may be practiced other than as specifically described herein.

What is claimed is:
 1. An apparatus for determining a cardiovascularparameter comprising: a processing unit to: receive an input signalcorresponding to an arterial blood pressure measurement over an intervalthat covers at least one cardiac cycle; determine a propagation time ofthe input signal; and determine an estimate of the cardiovascularparameter using the propagation time.
 2. The apparatus as defined inclaim 1 wherein the processing unit determines at least one statisticalmoment of the input signal.
 3. The apparatus as defined in claim 2wherein the processing unit determines an estimate of the cardiovascularparameter using the at least one statistical moment.
 4. The apparatus asdefined in claim 2 wherein the at least one statistical moment of theinput signal is selected from a group consisting of a statistical momenthaving an order greater than two, the kurtosis of the input signal, theskeweness of the input signal and a standard deviation of the inputsignal.
 5. The apparatus as defined in claim 1 wherein thecardiovascular parameter is selected from a group consisting of arterialcompliance, vascular resistance, cardiac output and stroke volume. 6.The apparatus as defined in claim 1 wherein the processing unitdetermines a propagation time of the input signal by determining atransit time between a reference signal detected near a heart of asubject and a peripheral arterial signal detected near an artery of thesubject.
 7. The apparatus as defined in claim 6 wherein the referencesignal is selected from a group consisting of an electro-cardiogrammeasurement, a central aortic pressure measurement, a transthoracicbioimpedance measurement and a Doppler ultrasound blood velocitymeasurement.
 8. The apparatus as defined in claim 6 wherein theperipheral arterial signal is selected from a group consisting of anarterial blood pressure measurement, an optical oximetry measurementthat measures the oxygen saturation of the blood of the subject, aperipheral bioimpedance measurement and a Doppler ultrasound bloodvelocity measurement.
 9. The apparatus as defined in claim 1 wherein theprocessing unit determines an estimate of the cardiovascular parameterusing a standard deviation of the input signal.
 10. The apparatus asdefined in claim 1 wherein the processing unit receives ananthropometric parameter of the subject.
 11. The apparatus as defined inclaim 10 wherein the processing unit determines an estimate of thecardiovascular parameter using the propagation time and theanthropometric parameter.
 12. The apparatus as defined in claim 10wherein the processing unit estimates an arterial compliance value usingthe propagation time and the anthropometric parameter.
 13. The apparatusas defined in claim 12 further comprising estimating a stroke volumeusing the arterial compliance value and a standard deviation of theinput signal.
 14. The apparatus as defined in claim 13 furthercomprising: receiving a heart rate measurement of a subject; andestimating cardiac output using the heart rate measurement and thestroke volume.
 15. The apparatus as defined in claim 14 furthercomprising estimating cardiac output using the arterial compliance andthe standard deviation.
 16. The apparatus as defined in claim 15 furthercomprising: receiving a calibration cardiac output value; andcalculating a calibration constant as a quotient between the calibrationcardiac output estimate and the product of the heart rate, the arterialcompliance and the standard deviation.
 17. The apparatus as defined inclaim 11 wherein estimating an arterial compliance value furthercomprises: determining an approximating function relating to a pluralityof reference measurements to arterial compliance, wherein theapproximating function is a function of the propagation time of theinput signal and the anthropometric parameter; and estimating thearterial compliance value of the subject by evaluating the approximatingfunction with the propagation time of the input signal and theanthropometric parameter.
 18. The method as defined in claim 1 furthercomprising: calculating a component propagation time value for each ofthe plurality of cardiac cycles; computing a composite propagation timevalue as an average of the component propagation time values; and usingthe composite propagation time value in calculating an estimate of thecardiovascular parameter.
 19. A machine-readable medium that providesinstructions, which when executed by a processor, cause the processor todetermining a cardiovascular parameter comprising: receiving an inputsignal corresponding to an arterial blood pressure measurement over aninterval that covers at least one cardiac cycle; determining apropagation time of the input signal; and determining an estimate of thecardiovascular parameter using the propagation time.